Finite Group Databasebeta

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C5×C9×D185 #30659254

order16650
isoclinismisoclinic class of D185
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D185
unambiguous semidirect productC5⋊(C5×C9×D37)

Splittings

Fitting, HallC52×C9×C37 ⋊ C2
derivedC5×C37 ⋊ C2×C5×C9
HallC52×C37 ⋊ C2×C9
HallC9×C37 ⋊ C5×D5
HallC52×C9 ⋊ D37
SylowC37 ⋊ C5×C9×D5
SylowC52 ⋊ C9×D37

Subgroups

subgroupG/H
center, hypercenterC5×C9D185
commutator, hypocenterC5×C37C2×C5×C9
FrattiniC3C3×C5×D185
FittingC52×C9×C37C2
socleC3×C52×C37C2×C3
prime radicalC3×C5×D185C3
cosocleC3×C5×C37C2×C3×C5
LCSG ▷ C5×C37
UCSC1 ◁ C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3330

Conjugacy classes & character table

4230 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×#10625191, C5×C9×#10625192, C5×C9×D5×D37, …
maximal normal subgroup ofC5×C9×#10625191, C5×C9×#10625192, C5×C9×D5×D37, …
maximal quotient ofC5×C9×Dic185, C2×C5×C9×D185

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 56);